Aparticularly beautiful note reaching your ear from a rare stradivarius violin has a wavelength of 39.1 cm. the room is slightly warm, so the speed of sound is 344 m/s. part a if the string's linear density is 0.550 g/m and the tension is 160 n , how long is the vibrating section of the violin string?

The wavelength of the note is . Since the speed of the wave is the speed of sound, , the frequency of the note is


Then, we know that the frequency of a vibrating string is related to the tension T of the string and its length L by

where  is the linear mass density of our string.
Using the value of the tension, T=160 N, and the frequency we just found, we can calculate the length of the string, L: